Showing papers on "Finite element method published in 1971"
Book•
01 Jan 1971
TL;DR: In this paper, the authors describe how people search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads, and instead they cope with some infectious bugs inside their computer.
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3,688 citations
TL;DR: In this paper, a generalized arc-length is introduced in the configuration-load space in order to facilitate the incremental computations near limit points, and the arc length is used as the loading parameter in some illustrative problems.
487 citations
TL;DR: In this article, it is shown that a solution for secondary rather than total field quantities can be obtained directly by using the finite element method to solve the electromagnetic energy minimization problem.
Abstract: Application of the finite element method to the solution of physical problems is based on minimization of energy; in the present case electromagnetic energy is minimized. Representation of a volume of space by a number of finite elements and description of field or potential distribution by a finite set of unknown values make it possible to replace the energy variational equation by matrix equations. It is shown that a solution for secondary rather than total field quantities can be obtained directly. Such a procedure has several advantages.Approximations are involved in using non-infinitesimal elements and finite meshes of elements. It is usually necessary to pay more attention to mesh size than texture (element size).Examples of induced polarization anomalies over two-dimensional models illustrate effects of topography and of a highly conducting layer above bodies of polarizable material. Computed electromagnetic anomalies of two-dimensional structures, with line source excitation, include the effects of adjacent conductors and magnetic conductors set in a less conductive half-space.
431 citations
TL;DR: In this article, a means is developed for simulation of realistic behavior of the interface between a backfill soil and a retaining wall in finite element analyses, and the interface behavior is shown from a series of laboratory tests to be dependent upon normal and shear stresses on the interface.
Abstract: A means is developed for simulation of realistic behavior of the interface between a backfill soil and a retaining wall in finite element analyses. The interface behavior is shown from a series of laboratory tests to be dependent upon normal and shear stresses on the interface. An analytical formulation is derived to fit the observed relationships and utilized to govern the behavior of a one-dimensional element which serves as the interface between two dimensional soil and retaining wall elements in finite element analyses. Analyses are presented of a typical retaining wall-backfill system with varying modes of wall behavior and degrees of wall roughness. Earth presure distributions before the ultimate conditions are reached are shown to be nonlinear. Ultimate conditions and general behavior of the system are shown to be in agreement with classical theory and previously observed behavior. An additional analysis is presented in which the exact construction sequence of a retaining-wall backfill system is simulated.
369 citations
TL;DR: In this article, a selective integration scheme for evaluating the stiffness matrix of a quadratic thick shell element was proposed, in which each component of the strain energy was evaluated separately using a different Gaussian integration grid for each contribution.
Abstract: A quadratic thick shell element derived from a three-dimensional isoparametric element was first introduced by Ahmad and co-workers in 1968. This element was noted, however, to be relatively inefficient in representing bending deformations in thin shell or thin plate applications. The present paper outlines a selective integration scheme for evaluating the stiffness matrix of the element, in which each component of the strain energy is evaluated separately using a different Gaussian integration grid for each contribution. By this procedure, the excessive bending stiffness of the element, which results from the use of me quadratic interpolation functions, is avoided.
The improved performance of this element, as compared with the original thick shell element, is demonstrated by analyses of a variety of thin and thick shell problems. 1
320 citations
01 Jan 1971
TL;DR: A detailed study of the implementation of finite element methods for solving two-dimensional elliptic partial differential equations shows that much of the manipulation of the basis functions necessary in the derivation of the approximation equations can be done semi-symbolically rather than numerically as is usually done.
Abstract: : A detailed study of the implementation of finite element methods for solving two-dimensional elliptic partial differential equations is presented. Generation and storage schemes for triangular meshes are considered, and the use of irregular meshes for finite element methods is shown to be relatively inexpensive in terms of storage. The report demonstrates that much of the manipulation of the basis functions necessary in the derivation of the approximation equations can be done semi-symbolically rather than numerically as is usually done. Ordering algorithms, compact storage schemes, and efficient implementation of elimination methods are studied in connection with sparse systems of finite element equations. A Fortran code is included for the finite element solution of a class of elliptic boundary value problems, and numerical solutions of several problems are presented. Comparisons among different finite element methods, and between finite element methods and their competitors are included.
266 citations
TL;DR: In this article, a new type of finite element is introduced which embodies the inverse square root singularity of the stress distribution arising near a crack in an elastic medium, and the authors used this element near the crack tip in two typical cracked configurations, with meshes having as few as 250 degrees of freedom.
239 citations
237 citations
TL;DR: In this paper, a detailed study of the deformations and stresses produced in an elastic-perfectly plastic half-space indented by a rigid sphere was done using the finite element method, which covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold.
Abstract: Using the finite element method, a detailed study of the deformations and stresses produced in an elastic-perfectly plastic half-space indented by a rigid sphere was done. The analysis covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold. Experimental results available in the literature are in good agreement with the analysis. In solving repeatedly the large number of linear equations involved in the solution of the problem, it was found profitable, in order to save computer time, to modify the direct elimination method. This technique is described in some details in the paper.
236 citations
TL;DR: In this paper, a modified finite element method for solving problems of elastic bodies in contact is described, which could be extended to solve other than elastic problems, and sample results agree well with corresponding exact solutions.
221 citations
TL;DR: In this paper, the theory of conjugate approximations is used to obtain persistent approximation of stress fields in finite element approximation based on displacement and assumptions, and these consistent stresses are continuous across interelement boundaries and involve less mean error than those computed by the conventional approach.
Abstract: The theory of conjugate approximations is used to obtain persistent approximations of stress fields in finite element approximations based on displacement and assumptions. These consistent stresses are continuous across interelement boundaries and involve less mean error than those computed by the conventional approach. (Author)
Journal Article•
TL;DR: In this article, the authors developed a method of theoretical analysis based on the finite element method, with consideration of the effects of changes in the modulus of elasticity, yield stress and the coefficient of linear thermal expansion of the metal with temperature.
Abstract: It is well known that welding thermal stresses and resulting residual stresses influence the strength of welded construction, causing troubles such as brittle fracture, buckling and weld cracking. At the instant of welding, a limited portion of the welded joint is heated up to a very high temperature and cooled down to room temperature. In the thermal cycle which takes place, the temperature distribution changes with time and it affects the mechanical properties of the metals. In order to perform a reliable theoretical analysis, the above mentioned factors should be taken into account. The authors developed a method of theoretical analysis of this problem based on the finite element method, with consideration of the effects of changes in the modulus of elasticity, yield stress and the coefficient of linear thermal expansion of the metal with temperature. They analysed thermal transient stresses induced in a butt weld under a moving electrode and also in a fillet weld in the courses of the first and second beads and obtained various information on thermal stress history in the process of welding. Examples verifying usefulness of the method are cited.
TL;DR: In this article, a nonconforming displacement triangular finite element with quadratically varying displacements for use in plate-bending problems is derived, and the element corresponds with a known constant-bending-moment element and provides, in consequence, an over-estimate of the influence coefficients.
Abstract: A non-conforming displacement triangular finite element is derived with quadratically varying displacements for use in plate-bending problems. It is shown that the element corresponds with a known constant-bending-moment element and provides, in consequence, an over-estimate of the influence coefficients. Convergence is also assured in advancing to successively finer mesh sizes. A few simple test problems are computed so as to illustrate the kind of accuracy which can be expected.
TL;DR: In this article, the authors used plate and acoustic finite elements to simulate the behavior of a window-room system and found that the room response is dominated by the volume displacing and plane wave depth modes.
TL;DR: In this article, a three-dimensional equilibrium finite element analysis is used to obtain approximate stress solutions for some finite symmetric laminates under inplane loading, based on a complementary energy formulation.
Abstract: A three-dimensional equilibrium finite element analysis is used to obtain approximate stress solutions for some finite symmetric laminates under inplane loading. The analysis is based on a comple mentary energy formulation. Obtained stress solutions at the center section of the laminate are compared with solutions for uniform axial strain that are available in the literature. A comparison of the stress distributions obtained at the center and end sections of the laminate shows that a large τyz stress can occur at the end section and a large τxz can occur at the center section. The influence of laminate stacking sequence on the predicted σz is also presented.
TL;DR: In this paper, a finite element analysis technique which includes the effects of transverse shear deformation and is readily adaptable to arbitrary laminated plates is described, where the displacement formulation is based on a refined theory for laminates which allows the deformed normal to rotate to include transverse deformation.
Abstract: A finite-element analysis technique which includes the effects of transverse shear deformation and is readily adaptable to arbitrary laminated plates is described. The discrete element employed is a rectangle with 28 degrees-of-freedom which include extension, bending, and transverse shear deformation states. The displacement formulation is based on a refined theory for laminates which allows the deformed normal to rotate to include transverse shear deformations. Results for plate deformations and internal stress distributions, including transverse shear stresses, are shown to compare quantitatively with the theory of elasticity for selected example problems. Additional results for laminate deformation behavior are in good agreement with the shear deformation theory of Ambartsumyan. The method described can easily be incorporated into existing matrix analysis schemes which can then be used with confidence in analyzing advanced composite structures.
TL;DR: In this article, a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods is presented. But the method is not suitable for the case of a beam and a plate vibration problem.
Abstract: Finite element procedures usually require more degrees of freedom for a specified accuracy than does a classical Ritz procedure if suitable coordinate functions are available. This paper develops a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods. This hybrid method preserves much of the flexibility of the finite element method while increasing the solution accuracy for a specified system order. The method is illustrated by examination of a beam and a plate vibration problem.
TL;DR: In this paper, a method developed previously for an analysis of the two-dimensional excitation of an elastic cylindrical shell by a transverse, transient acoustic wave is extended to three-dimensional applicability.
Abstract: A method developed previously for an analysis of the two‐dimensional excitation of an elastic cylindrical shell by a transverse, transient acoustic wave is extended to three‐dimensional applicability. In addition, some fluid‐structure interaction approximations are presented that follow naturally from the rigorous development. Application to finite element analysis of the transient response of submerged structures is discussed.
TL;DR: In this paper, a finite element method for nonsteady flow of groundwater with a free surface using the finite element approach has been developed. But the method is unconditionally, stable and therefore requires only a small number of time steps to reach the steady state.
Abstract: A new iterative, numerical approach to nonsteady flow of groundwater with a free surface using the finite element method has been developed. The method is unconditionally, stable and therefore requires only a small number of time steps to reach the steady state. It can handle problems in which the free surface is discontinuous and portions of the free surface are vertical or nearly vertical. Infiltration or evapotranspiration at the free surface is handled with ease, and the effect of the unsaturated zone can be taken into account indirectly by using the concept of delayed yield from storage. In addition to gravity drainage, the method takes into consideration storage due to the elastic properties of the saturated porous medium. In problems involving flow to a well operating at a prescribed rate, both storage in the well and the actual distribution of velocities along the well bore are taken into account. The method can be applied to a wide variety of problems involving complex boundaries and arbitrary degrees of heterogeneity and anisotropy. Several examples are included to demonstrate some of the features of this new approach.
TL;DR: In this paper, the structural response to rates of loads and dislocations (e.g. thermal strains) is studied and the following results are obtained; 1) six extremum properties of the solutions, which reduce the incremental problem to a quadratic programming problem; two of these properties are valid without restrictions; 2.
01 Dec 1971
TL;DR: In this article, a method based on the finite element method of discretisation and compatible with existing finite-element techniques is described for the solution of field problems in which the region of prime interest is embedded in an infinitely extending region where Laplace's equation holds.
Abstract: A new method, based on the finite-element method of discretisation and compatible with existing finite-element techniques, is described for the solution of field problems in which the region of prime interest is embedded in an infinitely extending region where Laplace's equation holds. The essence of this method lies in representing the infinitely extending region by a single finite element, which may be included in an element assembly descriptive of the finite region of major interest. No iterative computation is necessary, and the computing effort required for solution is essentially the same as that required for solving the interiorfield problem alone.
TL;DR: In this article, the authors extended the work of Ashwell and Sabir, assessing the power of curved finite elements by applying them to circular arches, and presented an element I based on the cylindrical shell element of Bogner et al.
TL;DR: In this paper, a numerical analysis in terms of finite elements of hybrid-mode propagation in closed microstrip is presented, and two modes with zero frequency cutoff are described; one is a quasi-TEM mode and the other a surface mode.
Abstract: A numerical analysis is presented in terms of finite elements of hybrid-mode propagation in closed microstrip. Two modes with zero frequency cutoff are described; one is a quasi-TEM mode and the other a surface mode. Also investigated is a third mode which corresponds to the lowest order waveguide mode in the absence of the strip.
TL;DR: In this paper, the nonlinear quasi-Poisson equation that describes static magnetic fields in saturable iron is solved approximately by minimizing the corresponding nonlinear energy functional, performed by means of the method of finite elements, using firstorder elements and a quadratically convergent iterative solution method.
Abstract: The nonlinear quasi-Poisson equation that describes static magnetic fields in saturable iron is solved approximately by minimizing the corresponding nonlinear energy functional. The minimization is performed by means of the method of finite elements, using firstorder elements and a quadratically convergent iterative solution method. The method is applied to a turboalternator and used to predict all the normal shop-floor test results. Excellent agreement is found between experimental and computed values. Computing times are found to be extremely fast, and it is concluded that this method is capable of producing results comparable to those obtained by finite difference methods, but at very much reduced cost.
TL;DR: In this paper, the finite element displacement method is used to investigate the flexural vibration characteristics of curved sandwich beams and various parametric studies are made to investigate their effect on the natural frequencies of curved clamped-clamped sandwich beams.
TL;DR: In this article, the bending analysis of reinforced concrete slabs by the finite element method is presented, which concentrates on the nonlinear behavior due to progressive cracking of a slab and does not include post-yield behavior.
Abstract: The bending analysis of reinforced concrete slabs by the finite element method is presented. The analysis concentrates on the nonlinear behavior due to progressive cracking of a slab and does not include post-yield behavior. The Branson and Beeby methods are explored for estimating the rigidity of a cracked concrete region. The latter is found to yield better results. In order to deal with cracking in any arbitrary direction, suggestions are made for the transformation of the matrix of flexural rigidities and for the determination of equivalent steel areas with respect to the orientation of the cracks in a region. Some results are presented to demonstrate the proposed method.
TL;DR: In this paper, a geometrically nonlinear dynamic analysis of shells of revolution under symmetric and asymmetric loads is presented, and the nonlinear strain energy expression is evaluated using linear functions for all displacements.
Abstract: A formulation and computer program is developed for the geometrically nonlinear dynamic analysis of shells of revolution under symmetric and asymmetric loads. The nonlinear strain energy expression is evaluated using linear functions for all displacements. Five different procedures are examined for solving the equations of equilibrium, with Houbolt's method proving to be the most suitable. Solutions are presented for the symmetrical and asymmetrical buckling of shallow caps under step pressure loadings and a wide variety of other problems including some highly nonlinear ones.
TL;DR: In this article, large strain elastoplastic analysis by finite element method, using variational principles to derive equilibrium equations is presented. But the analysis is restricted to two dimensional structures.
Abstract: Two dimensional structures large strain elastoplastic analysis by finite element method, using variational principles to derive equilibrium equations
TL;DR: In this paper, a theory for the determination of the free vibration characteristics of vertical, thin, circular cylindrical shells, partially or completely filled with stationary liquid, is presented for determining whether a shell may be uniform or non-uniform.